Consider a homebuyer/investor who plans to buy a new house, the price of which i

Question

Consider a homebuyer/investor who plans to buy a new house, the price of which is 1 million dollars. Suppose the buyer does not have any initial savings for the down payment. To buy the house, he needs to borrow $ 1 million from a bank in the form of a mortgage loan. The mortgage is a 30-year-fixed-rate mortgage. After buying the house, the buyer budget is $ 50,000 per year. That is, if the mortgage asks him to repay more than $ 50,000 per year (this happens when the interest rate is too high), then he cannot afford it and would choose not to buy this house. Derive the investment of this buyer as a function of interest rate r.

Explanation / Answer

Cost of house = 1 million $
We know, R = P × r / [1 - (1 + r)-n] , where R = monthly payment , r = interest rate , n = number of period, P= principle
n = 30 *12 = 360
R = 50000/12 = 4166.67 $
=> R = P × r / [1 - (1 + r)-n]

=> 4166.67 = 1000000 * r / [1 - (1 + r)-360]   (Ans)
=> 4166.67 = 1000000 * r/ [1 - (1 + r)-n]

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